Path: ...!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: olcott Newsgroups: comp.theory Subject: Re: No decider is ever accountable for the behavior of the computation that itself is contained within Date: Tue, 30 Jul 2024 18:20:43 -0500 Organization: A noiseless patient Spider Lines: 49 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Wed, 31 Jul 2024 01:20:44 +0200 (CEST) Injection-Info: dont-email.me; posting-host="d6c56e3cc0e766a5f243fbbf3db0d44a"; logging-data="1315783"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+wUpKIIn7QBZyiRj8E05zu" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:wmMsxokcC0Jnffhs/NUux6QOuYw= In-Reply-To: Content-Language: en-US Bytes: 3048 On 7/30/2024 1:56 AM, Mikko wrote: > On 2024-07-29 16:32:00 +0000, olcott said: > >> On 7/28/2024 3:40 AM, Mikko wrote: >>> On 2024-07-27 14:21:50 +0000, olcott said: >>> >>>> On 7/27/2024 2:46 AM, Mikko wrote: >>>>> On 2024-07-26 16:28:43 +0000, olcott said: >>>>> >>>>>> No decider is ever accountable for the behavior of the >>>>>> computation that itself is contained within. >>>>> >>>>> That claim is fully unjustified. How do you even define "accountable" >>>>> in the context of computations, automata, and deciders? >>>> >>>> int sum(int x, int y){ return x + y; } >>>> sum(5,6) is not accountable for reporting sum(3,2). >>> >>> That claim is fully unjustified. How do you even define "accountable" >>> in the context of computations, automata, and deciders? >>> >>>> It computes the mapping from its input to the value of their sum. >>> >>> That's obvious but is it relevant? >>> >>>> HHH must compute the mapping from its input finite string >>>> of the x86 machine code of DDD to the behavior that this >>>> finite string specifies and then report on the halt status >>>> of this behavior. >>> >>> Now is that relevant? >> >> Halt deciders report the halt status on the basis >> of the behavior that a finite string input specifies. > > How is that relevant? > Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. *given an* *input of the function domain it can return the corresponding output* https://en.wikipedia.org/wiki/Computable_function -- Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius hits a target no one else can see." Arthur Schopenhauer